Impulse-Momentum Theorem
'What is Impulse-Momentum Theorem' The impulse-momentum theorem can be summarized and explained with the following equation: J = ΔP = P2 - P1 J = Impulse P = momentum The impulse of an object is equal to the change in it's momentum. 'General info on Momentum' Momentum is P = mv! When an object has a mass and velocity, it has momentum. Since mass(m) is measured in kilogramkg and velocity(v) is measured in meters per secondm/s, momentum(P) is measured in kg*m/s. The mass and velocity is directly proportional to the momentum. 'Other Ways to find Impulse' J = FΔt or J = mΔv J = Impulse, F = Force, t = time (Δt = change in time), m = mass, v = velocity/speed (Δv= change in velocity/speed) 'Impulse's Unit' Impulse is measured in newton-second (N s) J = FΔt --> with force being measured in Newton(N) and delta time (Δt) in seconds(s), the units for impulse is s. FN * Δts = J's' Because mkg * Δvm/s can also be used to find the impulse(J) of an object, people might assume that impulse is measured in kg*m/s. Impulse can be measured in kg*m/s, but because momentum is usually measured in kg*m/s (pkg*m/s= mkg * vm/s), impulse is established to be measured with newton-seconds. 'Origin of Impulse-Momentum Theorem' There are no specific records as to who discovered the impulse-momentum theorum or when it was discovered. All we know is that it was derived from Newton's Second Law of Motion (F = ma). Other equations necessary to derived the impulse-momentum theorem are (a = Δv/Δt) and (P = mv). 'Relating to Newton's Second Law of Motion' Newton's Second Law of Motion: F = ma Since acceleration (a) is equal to Δv/Δt you can replace the acceleration (a) in Newton's Second Law of Motion with Δv/Δt to get F = (mΔv)/Δt To get rid of the fraction (or division), you can multiply both side with Δt and then the equation will become FΔt = mΔv mΔv = m(v2 - v1) = mv2 - mv1, and since {mv2 = P2} and {mv1 = P1} then FΔt = mΔv = P2 - P1 we can now conclude that J = FΔt, J = mΔv, or J = P2 - P1 !!! F = Force, m = mass, a = acceleration v = velocity/speed P = momentum 'Lets Review' Examples Stopping Cart Problem Question A cart with a mass of 1.1 x 10^3 kg is moving with a speed of 1.7 x 10^2 m/s. The impulse required to bring the car to rest is? Answer J = ΔP = mΔv m = 1.1 x 10^3 kg, v(i)= 1.7 x 10^2 m/s, v(f)= 0.0 m/s J = 1.1 x 10^3 kg x (1.7 x 10^2 m/s - 0.0 m/s) J = 1.87 x 10^5 N s Car Collision Problem Question What is the impulse of car 'A' during the collision? Answer J = mΔv You can see that the final picture on the right shows Car 'A' moving to the left when it was moving to the right in the beginning (refer to the 1st pic) at 4m/s. Since it changed direction, the final velocity/speed is actually -4m/s, while the initial velocity/speed is +8m/s. m = 2000kg, v(i) = 8m/s, v(f) = -4m/s J = mΔv = m(v(f)-v(i)) J = 2000kg(-4m/s-8m/s) J = 2000kg(-12m/s) J = -24000s Try it Yourself 1. The magnitude of an object's momentum is 23kg*m/s. If the velocity of that object is doubled, the new momentum of the object is? 2. A mother pushed a child on a swing by exerting 15N force over a time of .3s. What impulse is delivered to the child? 3. An impulse of J is applied to an object. The change in the momentum of the object is? # J # 2J # J/2 # 4J 4. Momentum may be expressed in # joules # watts # kilogram * meters per seconds-sq # Newton-seconds Others' Work The following links were all created by other students from LAB. They all have information related to impulse of momentum. 1. http://schools.wikia.com/wiki/Momentum 2. http://schools.wikia.com/wiki/Momentum:_Collisions 3. http://schools.wikia.com/wiki/Momentum_Conservation:_Explosions 'Reference' Resources 1. Zitzewits, Paul W. Glencoe PHYSICS Principles and Problems (1999) 2. Lazar, Miriam A. and Tarendashm, Albert S. Barron's Review Course Series Let's Review: Physics 3. Wong, May. Physics Binder 2005-2006. :D Images http://www.glenbrook.k12.il.us/gbssci/phys/Class/momentum/u4l1b.html (football) http://www.glenbrook.k12.il.us/gbssci/phys/Class/momentum/u4l1c.html (baseball) http://physics.k12albemarle.org/impulse/Quiz/testc.htm (Car Collision Problem)